Method and arrangement for generating binary sequences of random numbers

ABSTRACT

A method and arrangement for generating binary sequences of random numbers uses the principle of random selection of the path of photons on a beam splitter and generating a random number by using two detectors (D 1   0 , D 2   1 ) downstream from a beam splitter (ST 2 ). To generate photons, a light source (L) of a low power is used, and an additional beam splitter (ST 1 ) is connected upstream from the beam splitter (ST 2 ). The photons emitted by the light source (L) during a predefined measurement time are split by the beam splitters (ST 1 , ST 2 ) arranged one after the other in the beam path of the light source (L). The random sequence is generated when the splitting of the photons matches a predefined photon scheme.

FIELD OF THE INVENTION

The present invention relates to an arrangement and method forgenerating binary sequences of random numbers.

RELATED TECHNOLOGY

Random numbers are used in mathematical simulation of random processes,in random sampling and in cryptology in particular. Due to increasinghigh-bit-rate digital communications over publically accessiblecommunication channels, guaranteeing the confidentiality andauthenticity of the information transmitted has become a centralproblem. Good cryptographic codes are sequences of random binarynumbers. For secure encoding, preferably a random code of this type isselected; this code is as long as the message itself and is used onlyonce.

Essentially two different options are available for generating randomnumbers:

1. Pseudo-Random Numbers Generated by Mathematical Algorithms

Essentially, true random numbers cannot be generated by a computer,which operates completely deterministically. Therefore, the randomnumbers generated by mathematical algorithms and provided by manyprograms are never truly random. Pseudo-random numbers, developed from ashorter, truly random nucleus are an improvement.

In any case, however, a certain number of sequences that are not usablefrom the beginning (weak keys) must be expected in generatingpseudo-random numbers by the methods described above, and in any case,odd correlations must be expected.

2. Random Numbers Based on Physical Methods

These methods make use of the random character of certain physicalprocesses.

Even with the physical methods, there are those which are fundamentallydeterministic, but are so complex that they cannot be reproduced. Thiswould include, for example, a coin throw of heads or tails or lottomachines. These methods generate a deterministic chaos, which may beconsidered random because the initial conditions of the generator ingenerating each individual random number are always slightly differenteach time, without this difference being quantifiable. The physicalmethods also include elementary processes, such as those in quantummechanics. Such processes are naturally basically random. Random numbersgenerated by physical processes therefore come closer to the concept ofa random sequence than do random numbers generated by an algorithm.

There is a known solution utilizing the natural quantum process of theelectromagnetic noise of a resistor or a diode to generate random bitsequences (see Manfred Richter: “Ein Rauschgenerator zur Gewinnung vonquasiidealen Zufallszahlen für die stochastische Simulation” [A noisegenerator for generating quasi-ideal random numbers for stochasticsimulation], Dissertation RWTH Aachen; 1992).

However, such methods can be manipulated externally by superimposing anarbitrary predetermined “noise” on the quantum noise, e.g., fromincident electromagnetic waves. Since it is not easy to separate quantumnoise from such an externally imposed pseudo-noise, these methods arenot considered to be secure.

In addition, there are known methods of generating random numbers basedon radioactive decay processes (see Martin Gude: “Ein quasi-idealerGleichverteilungsgenerator basierend auf physikalischenZufallsphänomenen” [A quasi-ideal uniform distribution generator basedon physical random phenomena], Dissertation, RWTH Aachen 1987). Thismethod is very suitable for generating random sequences because of thehigh energy of the resulting particles, but in addition to the very realrisks, due in particular to the potentially harmful effect ofradioactive radiation on humans, there is also an irrational prejudiceagainst radioactivity on the part of some of the population, so thatradioactive processes cannot readily be used for random generation.

Another known method of generating random sequences is based on theprocess of selecting the path of individual photons on a beam splitter(see J. G. Rarity et al.: “Quantum random-number generation and keysharing” J. Mod. Opt. 41, p. 2435, 1994 which is hereby incorporated byreference herein). In this method, a light quantum is reflected ortransmitted on a semitransparent mirror, for example; two detectorsrecord the light quantum and their displays represent the “0” or “1” ofthe random sequence.

SUMMARY OF THE INVENTION

An object of the present invention is to provide a method and anarrangement for generating binary sequences of random numbers to avoidthe disadvantages described above, while being less expensive than priormethods and suitable for integration onto a chip card without any greatcomplexity.

The present invention provides a method of generating a binary sequenceof random numbers based on random selection of a path of photons on abeam splitter, the method including emitting photons or photon swarmsaccording to a randomness principle using a photon source, the photonsource including a low power light source; splitting the photons orphoton swarms emitted by the photon source during a measurement periodusing at least a first beam splitter and a second beam splitter disposedin a beam path of the light source, the second beam splitter beingdisposed downstream of the first beam splitter in a first downstreampath of the first beam splitter; detecting, in accordance with thesplitting, the photons or photon swarms from the splitting using afirst, a second and a third detector connected to a detection device,the first detector being disposed in a second downstream path of thefirst beam splitter, the second detector being disposed in a thirddownstream path of the second beam splitter, the third detector beingdisposed in a fourth downstream path of the second beam splitter;generating a random number when the photons or photon swarms detected atthe first, second and third detectors together correspond to apredefined photon scheme, the photon scheme including generating arandom number when only one of the second and third detectors registersa detection of the photons or photon swarms.

The present invention also provides an apparatus for generating a binarysequence of random numbers, the apparatus including a low power lightsource including a photon source for emitting individual photons and/orphoton swarms according to a randomness principle; a first and a secondbeam splitter disposed downstream from the light source in a beam pathof the light source, the first beam splitter being disposed between thelight source and the second beam splitter; a first detector disposed ina downstream path of the first beam splitter; a second detector and athird detector disposed in a first and a second downstream path,respectively, of the second beam splitter; a detection device forgenerating the random numbers, the detection device being disposeddownstream from the first, second and third detectors, the detectiondevice including at least one counter and computer.

The method according to the present invention uses the known principleof selecting the path of individual photons on a beam splitter. With themethod according to the present invention, ultraviolet, visible orinfrared light strikes an optical beam splitter, e.g., a semitransparentmirror. Two detectors which can detect individual photons register thephotons and define the “0” or the “1” of the random sequence via thedisplays assigned to them and thus define the random sequence itself.

With the method according to the present invention, a photon source of alow power and thus also small dimension is used as light source Linstead of the photon source customary in the past, such as anattenuated laser beam source. For example, attenuated laser diodes,normal diodes (LEDs), thermal light sources such as halogen lamps,spectral lamps or pinched light sources are suitable. In addition,according to the present invention, a first beam splitter ST1,preferably a trigger beam splitter, is inserted into the beam path oflight source L upstream from second beam splitter ST2. Thephotons/photon swarms emitted during a predefined measurement time bylight source L according to the random principle are split by beamsplitters ST1 and ST2 arranged in the beam path of light source L andare detected by detectors (trigger detector DT for beam splitter ST1 anddetectors D1 ₀ and D2 ₁ for beam splitter ST2) downstream from beamsplitters ST1 and ST1 according to the split.

Detectors DT, D1 ₀ and D2 ₁ are connected to detection unit E. A randomnumber is generated only if the photons registered at the individualdetectors DT, D1 ₀ and D2 ₁ correspond in their totality to a previouslydefined photon count scheme which has been input into the computer ofthe detection unit.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments

The present invention is explained in greater detail below withreference to the drawing, in which:

FIG. 1 shows a schematic representation of an arrangement for generatingbinary sequences.

DETAILED DESCRIPTION

Referring to FIG. 1, light source L has such a weak light intensity thatit emits individual photons or it always emits photon swarms of nphotons with a certain probability. These photon swarms are then eitherresolved in detectors DT, D1 ₀ and D2 ₁ or counted as a whole as asingle result. Probability p_(n) that n photons will arrive at thedetector at the same time or will be counted as a single result isdescribed by a Poisson distribution. $\begin{matrix}{p_{n} = {\frac{{\overset{\_}{n}}^{n}}{n!}e^{- \overset{\_}{n}}}} & (1)\end{matrix}${overscore (n)} is the average number of photons at the detector permeasurement time. Although the light source has different statistics ifit is thermal light (halogen lamp), chaotic light (spectral line) orlaser light, equation (1) applies to all these light sources as long asthe coherent time of a thermal or chaotic source is short in comparisonwith the measurement time of the detector. Equation (1) always appliesto laser light. With a simple beam splitter with two detectors, asillustrated by beam splitter ST2 and detectors D1 ₀ and D2 ₁ in FIG. 1,the electronics of the counting processes are set up so that a result isonly ever counted when only one of detectors D1 ₀ or D2 ₁ responds. Ifboth detectors D1 ₀ and D2 ₁ respond within the measurement time, thecounting event is discarded. If a swarm of photons is split on beamsplitter ST2, the result is not used. A counting event is used only ifthe swarm enters detector D1 ₀ completely or enters detector D2 ₁completely and is counted. With a swarm of n photons, this means thatonly 2 of n+1 events are counted, and therefore, equation (1) is to bemultiplied by $\frac{2}{n + 1}$to describe the probability with which counting events occur with aphoton swarm. Therefore, probability p_(n) that a usable counting eventwill occur at an average photon count {overscore (n)} is as follows forthe simple beam splitter, corresponding to beam splitter ST2, and one ofthe light sources L of a low power described above $\begin{matrix}{p_{n}^{(1)} = {\frac{{\overset{\_}{n}}^{n}}{n!}{e^{- \overset{\_}{n}} \cdot \frac{2}{n + 1}}\quad{simple}\quad{beam}\quad{splitter}}} & (2)\end{matrix}$

According to the present invention, another beam splitter ST1,preferably a trigger beam splitter, is connected upstream from simplebeam splitter ST2 (FIG. 1). As in the first case, the electroniccounters of both detectors D1 ₀ and D2 ₁ are connected so that a randomnumber is determined only when only one or only the other detector D1 ₀or D2 ₁ responds. In addition, however, trigger detector DT of beamsplitter ST1 must not respond in this case. Transit time effects betweentrigger detector DT of first beam splitter ST1 and detectors D1 ₀ and D2₁ of second beam splitter ST2 are compensated optically orelectronically. If there is a swarm of n photons and at least one photonof the swarm reaches trigger detector DT, the event is not counted. Anevent is counted as (0) or (1) only if no photon goes over first beamsplitter ST1 to trigger detector DT and also if all n photons at secondbeam splitter ST2 go either completely to detector D1 ₀ or completely todetector D2 ₁. The probability that no photon of the swarm will go totrigger detector DT and the rest will go completely to one of detectorsD1 ₀ or D2 ₁ is 4/((n+1)(n+2)), i.e., the probability p_(n) ⁽²⁾ that acounting event will occur with a swarm of n photons is $\begin{matrix}{p_{n}^{(2)} = {\frac{{\overset{\_}{n}}^{n}}{n!}{e^{- \overset{\_}{n}} \cdot \frac{4}{( {n + 1} )( {n + 2} )}}\begin{matrix}{{beam}\quad{splitter}\quad{ST2}\quad{with}} \\{{beam}\quad{splitter}\quad{ST1}\quad{connected}\quad{upstream}}\end{matrix}}} & (3)\end{matrix}$

Equation (3) applies to the case when beam splitter ST1 has splittingratio 1/3:2/3, but beam splitter ST2 has splitting ratio 1/2:1/2. Inthis case, three detectors DT, D1 ₀ and D2 ₁ are weighted equally. Othersplitting ratios are possible, but they alter the probabilitiesaccording to equation (3).

The method according to the present invention makes it progressivelyless likely that, with an increasing number n of photons emitted duringa predefined measurement time, an n-photon swarm will lead to a countingevent and thus to a random number. However, there is an increase in theprobability that the ideal case in terms of quantum mechanics willoccur, namely generation of a random event by a single photon on thebeam splitter. Multi-photon events, which in the limit case of greaterthan n go into the conventional state, are suppressed. Thus, accordingto the present invention, weak lasers, chaotic or thermal light sourcescan be used as random generators.

An arrangement of more than one trigger beam splitter in the beam pathbetween light source L and beam splitter ST2 is also conceivable. Thetrigger detectors of these additional trigger beam splitters are alsoconnected to detection device E. In such an embodiment, the photonsdetected during the predefined measurement time are registered in thedetection device in accordance with their assignment to the individualtrigger beam splitters (including beam splitter ST2) and are likewisecompared with a predetermined photon scheme stored in detection deviceE. In such an embodiment, photon swarms are suppressed to an evengreater extent. Random events are recorded, for example, only when noneof the trigger detectors responds.

Another defined or variable photon scheme may also be selected with anembodiment having multiple trigger detectors in the beam path of lightsource L. For example, the photon scheme may include the fact that thetrigger detector of every second trigger beam splitter must respond orthat only the trigger detector of the first and seventh trigger beamsplitter must respond. In each of these cases, the counting probabilityfor the photon swarm is reduced.

An interesting example is an arrangement according to FIG. 1, where therandom events at second beam splitter ST2 are counted only when one ormore photons are registered by trigger detector DT of beam splitter ST1.In this case, swarms with only one photon are not used at all for randomgeneration. Since detectors today also have some very unpleasantproperties, such as a low quantum efficiency and dead times, thetrade-in for additional trigger beam splitters is also additionalelectronic problems and higher costs. Thus, in practice, preferably onlyone additional trigger beam splitter is used.

List of reference notation L light source ST1 first beam splitter(trigger beam splitter) ST2 second beam splitter E detection device DTtrigger detector of the first beam splitter D1₀, D2₁ detectors of thesecond beam splitter n number of photons emitted by the light sourceduring a de- fined measurement time

1. A method of generating a binary sequence of random numbers based onrandom selection of a path of photons on a beam splitter, the methodcomprising: emitting photons or photon swarms according to a randomnessprinciple using a photon source, the photon source including a low powerlight source; splitting the photons or photon swarms emitted by thephoton source during a measurement period using at least a first beamsplitter and a second beam splitter disposed in a beam path of the lightsource, the second beam splitter being disposed downstream of the firstbeam splitter in a first downstream path of the first beam splitter;detecting, in accordance with the splitting, the photons of photonswarms from the splitting using a first, a second and a third detectorconnected to a detection device, the first detector being disposed in asecond downstream path of the first beam splitter, the second detectorbeing disposed in a third downstream path of the second beam splitter,the third detector being disposed in a fourth downstream path of thesecond beam splitter; generating a random number when the photons orphoton swarms detected at the first, second and third detectors togethercorrespond to a predefined photon scheme, and photon scheme includinggenerating a random number when only one of the second and thirddetectors registers a detection of the photons of photon swarms.
 2. Themethod as recited in claim 1 wherein the photon scheme includesgenerating a random number when during the measurement period no photonof the photons of photon swarms is detected at the first detector and atleast one photon of the photons or photon swarms is detected at only oneof the second and third detectors.
 3. The method as recited in claim 1wherein the photon scheme includes generating a random number whenduring the measurement period at least one photon of the photons orphoton swarms is detected at the first detector and at least one photonof the photons or photon swarms is detected at only one of the secondand third detectors.
 4. The method as recited in claim 1 wherein the atleast a first and second beam splitters includes at least a third beamsplitter disposed in the beam path between the light source and thesecond beam splitter, each of the at least a third beam splitterincluding an associated fourth detector disposed in a respectivedownstream path of the associated at least a third beam splitter, thephoton scheme including generating a random number only when a photonswarms of the photons or photon swarms including a number of photonsdefined by the photon scheme is detected at the first, second, third andfourth detectors.
 5. An apparatus for generating a binary sequence ofrandom numbers, the apparatus comprising: a low power light sourceincluding a photon source for emitting individual photons and/or photonswarms according to a randomness principle; a first and a second beamsplitter disposed downstream from the light sources in a beam path ofthe light source, the first beam splitter being disposed between thelight source and the second beam splitter; a first detector disposed ina downstream path of the first beam splitter; a second detector andthird detector disposed in a first and a second downstream path,respectively, of the second beam splitter; and a detection device forgenerating the random numbers, the detection device being disposeddownstream from the first, second and third detectors, the detectiondevice including at least one counter and computer.
 6. The apparatus asrecited in claim 5 wherein the first beam splitter includes a triggerbeam splitter and the first detector includes a trigger detector.
 7. Theapparatus as recited in claim 5 wherein the photon source includes asattenuated laser.
 8. The apparatus as recited in claim 5 wherein thephoton source includes a thermal light source.
 9. The apparatus asrecited in claim 5 wherein the photon source includes a spectral lamp.10. The apparatus as recited in claim 5 wherein the photon sourceincludes a light emitting diode.
 11. The apparatus as recited in claim 5wherein the photon source includes a pinched light source.